Why wouldn't the חכמים let the alternative ones stand, unless they were operating on the premise that 'fixed, finite text' is the way it has to be?
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paqudaApr 25 '14 at 0:41

The חכמים may have thought that was ideal, but in reality, variant texts existed. Then again, we have a whole system of k'ri-ketiv\alternate versions, indicating that maybe they didn't think so at all.
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ShmuelApr 25 '14 at 0:45

In other words, if the חכמים thought a "fixed finite text" is ideal, why did they let the alternate spellings\pronunciations stand, instead of just eliminating the 'wrong' one entirely?
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ShmuelApr 25 '14 at 0:46

Torah sheBichtav refers to books written while there was still Nevua and\or the Jews lived in Israel with a Beit Mikdash. Torah sheBaal Peh refers to anything written after the end of this holy era, and also includes any discussion and interpretation of sheBichtav.

Let's flip the question around:

Why is Yehoshua (and the rest of Neviim Rishonim) not part of "Torah," as they appear to be a simple continuation of the story? If Devarim, which is Moshe's speech (and thus wasn't revealed at Sinai), is part of Torah, then why isn't Yehoshua or Shmuel, which are Yehoshua's and Shmuel's narrative and speeches, respectively?

The answer to this, and to your question, is that at some point in Jewish history some books were accepted as "super-holy" (or similar, can't really express it), and were raised to a new level. They were then categorized as such, and no new books were allowed to be added to them.

This happened in several stages. The first stage was for Torah, which was "closed" when the Jews entered Israel. The second stage was for Neviim, which was closed with Churban Bayit Rishon (appx) and the end of Nevua. And the third stage was Ketuvim, which was closed with Churban Bayit Sheini. (This also explains why Daniel, for example, is part of Ketuvim and not Neviim.) After the destruction of both Batei Mikdash, that era of holiness and prophecy was over, and no new books could be added to Torah sheBichtav at all.

@Shmuel actually the close was the Anshei Knesses Hagedolah at the start of the second temple era. That is why Esther was accepted but there are no Kesuvim for Chanukah
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sabbahillelApr 24 '14 at 11:26

Also, it's unclear when Esther was written\took place. Finally, even after the Churban there was still discussion about which books are "meTamei Yadiim" etc, indicating that canonization was a process that took some time to complete.
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ShmuelApr 24 '14 at 22:00

"in the hand of Malachi" - [Rashi] It was already delivered into his
hand for many days. From here, our Sages expounded in a baraitha of
Mechilta that all the prophets stood on Mount Sinai and there the
prophecies were delivered to them, and so [Isaiah (48:16)] says:
“From the time it was, there was I, and now, the Lord God has sent me,
[and His spirit].”

hence, just because it was written later does not mean it did not already exist in some form.

"Torah sheb'al peh" refers to the explanations that accompanied the 1st Five Books (Breishit - Devarim). This was eventually written into what we have as the mishna, with gemarrah being an explanation on this. I am uncertain if any of the books of either Nevi'im (Prophets) or Ketuvim (Writings) would even be considered "Torah Shebichtav" or they are a separate category.